Quantum RL and control policies

Choosing an action from an observed state

A variational policy is a circuit that takes the observed state as input angles and returns action probabilities as measurement outcomes. Training is ordinary REINFORCE: sample an action, collect the reward, and push the parameters toward actions that scored above the batch mean. The circuit replaces the policy network and nothing else about the loop changes.

Because the state enters as input angles rather than as trainable parameters, the data parameters have to be held fixed while the weights move. That split is what separates a policy from a Born machine, which trains every angle it has.

The ZKSF billing screen showing available credit, spend by tier and daily spend as a bar chart, which is how a training loop is budgeted — Per-task rates matter here more than anywhere else on this page: one decision is one task. Open the console

Method: Variational quantum policy trained by REINFORCE
Who runs this: Control systems, scheduling, operations research
Classical baseline: A random policy, at 0.533 mean return
Structural limit: One circuit per decision: an episode of 1,000 steps is 1,000 jobs

Run on our engines

A two-qubit policy with four trainable weights, trained by REINFORCE over 60 decisions, then probed at two states on hardware. Submitted to each kind of compute we offer, on 18 September 2026. Every figure below is a real job on the service, priced as any customer would be priced.

Engine	Kind	Qubits	Result	Cost
exact.cpu	CPU	2	mean return 0.611 over the last three batches, against 0.533 for a random policy	$0.0540
exact.gpu	GPU	2	P(action 1) 0.158 and 0.624 at the same two probe states certificate	$0.0002
qpu.rigetti	QPU	2	P(action 1) 0.199 and 0.650 at two probe states, against 0.049 and 0.708 noiseless	$1.4500
qpu.iqm.garnet	QPU	2	P(action 1) 0.177 and 0.576 at the same two probe states certificate	$3.5000

A note on the hardware certificates: they state Hellinger fidelity against the exact distribution. For an optimisation circuit that distribution is spread across many outcomes rather than concentrated on one, so the figure is low by construction and is not a measure of whether the device found a good answer. The result column above is.

The same problem is yours to run: every instance here is seeded, so it rebuilds exactly. Open the console and a cost estimate is free before anything executes.

540 circuits over 60 decisions. The random baseline returns 0.533 on this task rather than 0.5, which is the sampling spread at that number of decisions.

On hardware both probes moved toward 0.5, by 0.15 and 0.06, which is the readout floor. The same weights on a noiseless statevector separate the two states the same way, so the device reproduced the policy it was given.

Three engines now hold the same policy. Every one of them puts the two probe states on opposite sides of 0.5 and in the same order, 0.158 and 0.624 on GPU, 0.199 and 0.650 on Rigetti, 0.177 and 0.576 on IQM Garnet, so the decision the policy makes survives the move between them and only the margin changes.

The GPU row is two runs at the platform floor of $0.0001 each. That floor is doing the work, not the tier: GPU bills at $3.00 an hour and CPU at $0.69, and neither rate reaches a cent on a circuit this small.

What the makers say it is for

The clearest industry statement about this shape of workload is not about policies at all. Quandela and NVIDIA describe a hybrid model in which the GPU remains at the core of the AI workflow and the quantum processor acts as a specialised accelerator for specific parts of it, reached over a low-latency link.

A policy loop is that model at its most demanding, because the quantum part is called once per decision rather than once per batch. The round trip is the cost, and the table below prices it.

The reverse direction is also being built. Rigetti and Quantum Machines have reported applying AI to the calibration of a quantum computer, which is machine learning operating the device rather than running on it. Pasqal publishes an introduction to quantum AI aimed at business leaders, which is a fair guide to how the field is being presented to buyers.

Where this stops

Every decision is one circuit and one job, so an episode length is a job count
60 decisions is a small sample: a margin of 0.611 against 0.533 sits inside the spread of that sample size, and separating them needs hundreds of episodes across several seeds
Gradients here are central differences, which cost two evaluations per parameter

The structural limit above does not move when a benchmark is re-run. Everything else on this page is a measurement, and a measurement can be repeated.

Run it yourself

Every figure above is from a job billed on the production service. Load the same circuits into the console, change the instance to your own data, and export a certificate for your own run rather than citing ours.

The argument behind these numbers, at length: Quantum machine learning on simulators and real quantum hardware.

Read the docs Benchmark methodology

Other AI use cases

QCBM and quantum generative models